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Strong asymptotics of two-point Padé approximants for power-like multivalued functions. (English. Russian original) Zbl 1300.41009
Dokl. Math. 89, No. 2, 165-168 (2014); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 455, No. 1, 138-141 (2014).
The authors study two point Padé approximants constructed from two germs \( \omega _{0}\) and \(\omega _{\infty }\) of the same multivalued analytic function of the form \[ w\left( z\right) =w\left( z;\mathcal{A},\alpha \right) :=\prod \limits_{j=1}^{\infty }\left( z-a_{j}\right) ^{\alpha _{j}}, \] where \(p\geq 2,\) \(\alpha _{j}\in \mathbb{C}/\mathbb{Z}\), \(\sum_{j=1}^{p}\alpha _{j}=0\), \(\alpha _{1},\alpha _{2},\ldots,\alpha _{p}\) are any different points in \(\mathbb{C}^{\ast }=\mathbb{C}/\left \{ 0\right \}\), \( \mathcal{A=} \{ a_{1,}a_{2},\ldots,a_{p}\}\), and \(\alpha =\{ \alpha _{1},\alpha _{2},\ldots,\alpha _{p}\}\). They obtain a second order differential equation with polynomial accessory parameters and solve the equation.

MSC:
41A21 Padé approximation
41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)
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